Perform a statistical enquiry that will either prove or disapprove my hypothesis.

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Introduction

Statistical Enquiry

Aim:To perform a statistical enquiry that will either prove or disapprove my hypothesis.

Hypothesis: Higher the persons IQ, higher the SAT results

Method: In this statistical enquiry, I aim to find out if people that have higher IQ have better results in English. For me to be able to perform the enquiry I had to have data about the IQ of students. I have a database of pupils of Mayfield High School, which is a fictional school based on data from real schools, complete with their IQ. Because it is based on real schools, the data will be reliable and accurate enough for me to draw a conclusion from the enquiry. There are 1183 pupils at Mayfield High School- I decided to compare 10% of general population. This is roughly 100 pupils. The hundred people I get from the general population will be my sample. Since there are different strata’s in my data, I had to find out what number of boys or girls from each year group I am going to take from my hundred samples. For that I used stratified sampling.

Stratified Sampling

Students in Mayfield high school are the population of the school. The population of the school are the pupils that are being studied. Since in Mayfield High School there are 1183 pupils, it would be very impractical for me to study and compare all of the data. I have to take a sample- a smaller group of people from general population. I have decided to take 10% of general population as my

sample.

Year Group

Number of boys

Number of girls

7

151

131

8

145

125

9

118

143

10

106

94

11

84

86

In the Mayfield School database there are different strata’s for the data. Strata are distinctive non-overlapping subsets of the population.

To further investigate my data, I decided to perform summary statistic on the Years 10 and 11. this will give me further knowledge of the population of the school and what are there averages. This will be my subgroup.

Subgroup

Frequency tables of year 10 and 11

I have decided to do everything for the year 11 and 12 as I did for the general data of my sample. First I have to do the frequency tables.

Frequency table of IQ

I can not do the frequency table on the IQ due to the high range of possible values. Instead I do the group frequency of the IQ. Everything is done the same as for the main data. The only difference is that the data is much smaller.

IQ

Frequency

70-79

2

80-89

4

90-99

8

100-109

11

110-119

5

120-129

0

This table shows the frequency of the particular value in my data. As you can see there are several differences form my general sample data. For one thing, there I no student in years 10 and 11 that have IQ higher than 120. Also there is no very distinctive majority for any particular data. These differences can be shown by a frequency polygon.

As you can see, the difference from the order frequency polygon is that it has broader width. The frequency of the IQ values is more disturbed between them.

Frequency table of SAT results

Since there aren’t any large ranges of values, I am able to use normal frequency table for SAT results data.

SAT levels

Frequency

1

0

2

2

3

7

4

14

5

8

My frequency table, like that for the general data, shows that predominant level is level 4. However, as with the Y10 and 11 tables, the frequency of the values is more disturbed.

I did the summary statistic to see what the average is of the population of that particular school. The results I got such as correlation coefficient and regression line are only relative to the particular population that gets this kind of averages. It might be that this school isn’t an average school in a country and that you will get a different results in other schools. While these results can be applied to this school, it is possible that they cannot be applied in different schools.

Evaluation

I performed a statistical enquiry using mathematical methods to improve or disapprove my hypothesis. I have completed my investigation successfully, proving my hypothesis. I used summary statistics in describing a population. I have calculated regression line and I have found out the correlation coefficient. This investigation was done thoroughly and accurately as I could possibly make it. I believe it was a success.

However, I believe there are certain ways I could improve the investigation. I know that IQ affects SAT results, but now I could try to see what other factors also affect the results. I could perform an investigation to see if amount of time spent studying or watching TV has any effect on the SAT results.

Also, I could see if this data could be applied to more schools than one. I could get a sample of schools from the entire country and see if there summary statistics match mine. I could find out if the Mayfield High School is an average school of the country.

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